Jie Han, Spanning trees in expanders

We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap forcing an $(n,d,\lambda)$-graph to be $T(n, \Delta)$-universal. In this talk, we introduce our recent work on this conjecture.